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rr t - - PowerPoint PPT Presentation

Apr 01, 2024 217 likes •311 views

rr trs s t rr t

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SLIDE 1

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷

❙❖❊✸✷✶✶✴✷ ❋❧✉✐❞ ▼❡❝❤❛♥✐❝s ❧❡❝t✉r❡ ✾

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SLIDE 2

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮

■♥ r❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s t❤❡ ✌♦✇ ✐s ✸✲❞ ✿ ✇❡ ❝♦✉❧❞ ✇r✐t❡ ✐t ❛s ✐♥ ❝②❧✐♥❞r✐❝❛❧ ♣♦❧❛r ❝♦♦r❞✐♥❛t❡s ✈ ❂ ✈r❫ r ✰ ✈✒❫ ✒ ✰ ✈③❫ ③ ✇❤❡r❡ ❫ r✱ ❫ ✒✱ ❫ ③ ❛r❡ ✉♥✐t ✈❡❝t♦rs ✐♥ r❛❞✐❛❧✱ t❛♥❣❡♥t✐❛❧✱ ❛①✐❛❧ ❞✐r❡❝t✐♦♥s✳ ❍♦✇❡✈❡r ✇❡ ❝❛♥ ♠❛❦❡ ❛ s✐♠♣❧✐❢②✐♥❣ ❛ss✉♠♣t✐♦♥ ❀ t❤❛t ✈ ✐s ❛ ❢♥✳ ♦❢ r ♦♥❧②✳ ❚❤✐s ✐s ❡q✉✐✈❛❧❡♥t t♦ ❛ss✉♠✐♥❣ ✿

✶ t❤❡ ❜❧❛❞❡s ❛r❡ ✐♥☞♥✐t❡❧② t❤✐♥ ④ ♣r❡ss✉r❡ ❞✐☛❡r❡♥❝❡ ❛❝r♦ss

❜❧❛❞❡ ♣r♦❞✉❝❡s t♦rq✉❡

✷ t❤❡ ✌♦✇ ✐s ❛①✐s②♠♠❡tr✐❝ ✭♥✉♠❜❡r ♦❢ ❜❧❛❞❡s ✦ ✶✮ ✸ ♥♦ ✈❛r✐❛t✐♦♥ ❛①✐❛❧❧②

slide-3
SLIDE 3

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❉❡☞♥❡ t❤❡ ❢♦❧❧♦✇✐♥❣ s②♠❜♦❧s ✿ ✈ ❂ ❛❜s♦❧✉t❡ ✈❡❧♦❝✐t② ✈✇ ❂ t❛♥❣❡♥t✐❛❧ ✭✇❤✐r❧✮ ✈❡❧♦❝✐t② ✈❢ ❂ ✌♦✇ ✈❡❧♦❝✐t② ✉ ❂ ✐♠♣❡❧❧❡r ✈❡❧♦❝✐t② ❞✉❡ t♦ ✦ ❂ ❛♥❣✉❧❛r r♦t❛t✐♦♥ ✈r ❂ ✈❡❧♦❝✐t② r❡❧❛t✐✈❡ t♦ ✐♠♣❡❧❧❡r ✈r✶ ❂ ✈✶ ✉✶

α 1 β 1 v r1 u 1 v w

1

v 1

slide-4
SLIDE 4

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮

❚❤✐s ✐s ✇❤❡r❡ ✇❤❡♥ t❤❡ ✌✉✐❞ ❡♥t❡rs ❛♥❞ ❧❡❛✈❡s ❛t t❤❡ ❛♥❣❧❡ t❤❡ ❜❧❛❞❡ ✐s s❡t✱ ✐✳❡✳ ☞✵ ❂ ☞ ✈❢ ✐s ♥♦r♠❛❧ t♦ t❤❡ ❝♦♥tr♦❧ s✉r❢❛❝❡✱ s♦ r❡❧❛t❡s t♦ t❤❡ ✌✉① ✐♥t♦ t❤❡ ❈✳❱✳ ✈✇ ✐s t❤❡ ✇❤✐r❧ ✈❡❧♦❝✐t② ❛t t❤❡ ❡♥tr② t♦ t❤❡ ❈✳❱✳

v r

1

u 1 v w1 v1 vf1

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SLIDE 5

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮

❲❡ ❦♥♦✇ t❤❛t ❛♣♣❧②✐♥❣ ❝♦♥s❡r✈❛t✐♦♥ ♦❢ ❧✐♥❡❛r ♠♦♠❡♥t✉♠ ✐♥ t❤❡ ✐♥t❡❣r❛❧ ❢♦r♠✉❧❛t✐♦♥ ❣✐✈❡s t❤❡ ❢♦r❝❡ ♦♥ ❛ ❜♦❞②✳ ❙✐♠✐❧❛r❧② ❢♦r r♦t❛t✐♥❣ ✌♦✇s ❚ ❈❱ ❂ ❩❩ ✭✚r ✂ ✈✮✈✿❞❆ ✐s t❤❡ ♥❡t t♦rq✉❡ ❲❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ t❤❡ t♦rq✉❡ ✐♥ t❤❡ ③ ❞✐r❡❝t✐♦♥ ✿ ❚③ ❂ ❩❩

♦✉t

✭✚r✈✇✮✈✿❞❆ ❩❩

✐♥

✭✚r✈✇✮✈✿❞❆ ❇✉t ❩❩ ✈✿❞❆ s♦ ❚③ ❂ ✭✚r✈✇✈❢ ❆✮✷ ✭✚r✈✇✈❢ ❆✮✶

slide-6
SLIDE 6

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❍♦✇❡✈❡r ❝♦♥s❡r✈✐♥❣ ♠❛ss ❣✐✈❡s t❤❡ ♠❡❛♥ ✌♦✇ ❴ ♠ ❂ ✭✚✈❢ ❆✮✶ ❂ ✭✚✈❢ ❆✮✷ ❙♦ ❚③ ❂ ❴ ♠ ❬r✷✈✇✷ r✶✈✇✶❪ P♦✇❡r ❂ ❚♦rq✉❡ ✂ ❆♥❣✉❧❛r ❱❡❧♦❝✐t②✱ s♦ P ❂ ❴ ♠✦ ❬r✷✈✇✷ r✶✈✇✶❪ ❆❧s♦ ✉ ❂ r✦ ❢♦r t❤❡ ✐♠♣❡❧❧❡r P ❂ ❴ ♠ ❬✉✷✈✇✷ ✉✶✈✇✶❪

slide-7
SLIDE 7

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❆s ❜❡❢♦r❡ ✇❡ ✇❛♥t t♦ ❜❡ ❛❜❧❡ t♦ ❡①♣r❡ss t❤✐s ✐♥ t❡r♠s ♦❢ t❤❡ ❤❡❛❞ ❍✐♠♣ ❂ P ❴ ♠❣ ❂ ✶ ❣ ✭✉✷✈✇✷ ✉✶✈✇✶✮ ④ ❊✉❧❡r✬s ❡q✉❛t✐♦♥ ❊①♣r❡ss t❤✐s ✉s✐♥❣ ❛❜s♦❧✉t❡ ✈❡❧♦❝✐t✐❡s ✈✇✶ ❂ ✈✶ ❝♦s ☛✶ ✈✷

r✶ ❂ ✉✷ ✶ ✰ ✈✷ ✶ ✷✉✶✈✶ ❝♦s ☛✶

α1 v r

1

u 1 v w1 v

1

α1

slide-8
SLIDE 8

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❈♦♠❜✐♥✐♥❣ t❤❡s❡ ❣✐✈❡s ✉✶✈✶ ❝♦s ☛✶ ❂ ✉✶✈✇✶ ❂ ✶ ✷

  • ✉✷

✶ ✈✷ r✶ ✰ ✈✷ ✶

✁ ❲❡ ❝❛♥ ✇r✐t❡ s✐♠✐❧❛r ❡①♣r❡ss✐♦♥s ❢♦r ❧♦❝❛t✐♦♥ ✷✳ ❙✉❜st✐t✉t✐♥❣ t❤❡s❡ ❍✐♠♣ ❂ ✈✷

✷ ✈✷ ✶

✷❣ ✰ ✉✷

✷ ✉✷ ✶

✷❣ ✰ ✈✷

r✶ ✈✷ r✷

✷❣

✈✷

✷ ✈✷ ✶

✷❣

✿ ✐♥❝r❡❛s❡ ✐♥ ❦✳❡✳ ♦❢ t❤❡ ✌✉✐❞ ✐♥ t❤❡ ✐♠♣❡❧❧❡r

✉✷

✷✉✷ ✶

✷❣

✿ ❡♥❡r❣② ✉s❡❞ ♣✉tt✐♥❣ ✌✉✐❞ ✐♥t♦ ❝✐r❝✉❧❛r ♠♦t✐♦♥ ❛❜♦✉t t❤❡ ✐♠♣❡❧❧❡r

✈✷

r✶✈✷ r✷

✷❣

✿ st❛t✐❝ ❤❡❛❞ ❣❛✐♥❡❞ ❞✉❡ t♦ r❡❞✉❝t✐♦♥ ✐♥ r❡❧❛t✐✈❡ ✈❡❧♦❝✐t② ❛s ✌✉✐❞ ❣♦❡s t❤r♦✉❣❤ ✐♠♣❡❧❧❡r

slide-9
SLIDE 9

❚✉r❜♦♠❛❝❤✐♥❡r② ④ ✷ ❘❡❛❧ t✉r❜♦♠❛❝❤✐♥❡s ✭❆✮ ❵◆♦ s❤♦❝❦✬ ❝♦♥❞✐t✐♦♥ ✭❆✮ ▼♦♠❡♥t✉♠ ❜❛❧❛♥❝❡ ✭❆✮ ❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❈❡♥tr✐❢✉❣❛❧ ✐♠♣❡❧❧❡r ✭❆✮

❘♦t❛t✐♥❣ ✇✐t❤ ❛♥❣✉❧❛r ✈❡❧♦❝✐t② ✦ ✮ ✉✶ ❂ r✶✦ ✉✷ ❂ r✷✦ ❚❤❡ ♠❛ss ✌♦✇ ❴ ♠ ❢♦r t❤✐♥ ❜❧❛❞❡s ❴ ♠ ❂ ✚✶✷✙r✶❜✶✈❢ ✶ ❂ ✚✷✷✙r✷❜✷✈❢ ✷ ■❢ t❤❡ ✌♦✇ ✐s ✐♥❝♦♠♣r❡ss✐❜❧❡ r✶❜✶✈❢ ✶ ❂ r✷❜✷✈❢ ✷

b1 b2